1. Chapter 5
Energy

2. Forms of Energy Mechanical Chemical Electromagnetic Nuclear
Focus for now
May be kinetic (associated with motion) or potential (associated with position)
Chemical
Electromagnetic
Nuclear

3. Some Energy Considerations
Energy can be transformed from one form to another
Essential to the study of physics, chemistry, biology, geology, astronomy
Can be used in place of Newton’s laws to solve certain problems more simply

4. Work 5.1 Provides a link between force and energy
The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement

5. Work, cont. F is the magnitude of the force
Δ x is the magnitude of the object’s displacement
q is the angle between
Only force parallel to movement does work!

6. Work, cont. This gives no information about Work is a scalar quantity
the time it took for the displacement to occur
the velocity or acceleration of the object
Work is a scalar quantity

7. Units of Work SI US Customary Newton • meter = Joule foot • pound
N • m = J
J = kg • m2 / s2
US Customary
foot • pound
ft • lb
no special name

8. More About Work
The work done by a force is zero when the force is perpendicular to the displacement
cos 90° = 0
If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force

9. More About Work, cont. Work can be positive or negative
Positive if the force and the displacement are in the same direction
Negative if the force and the displacement are in the opposite direction

10. When Work is Zero Displacement is horizontal Force is vertical
cos 90° = 0

11. Work Can Be Positive or Negative
Work is positive when lifting the box
Work would be negative if lowering the box
The force would still be upward, but the displacement would be downward

12. QQ 5.1

13. QQ 5.1 Answer
(c). The work done by the force is , where is the angle between the direction of the force and the direction of the displacement (positive x-direction). Thus, the work has its largest positive value in (c) where , the work done in (a) is zero since , the work done in (d) is negative since , and the work done is most negative in (b) where .

14. e.g. 5.1
An Eskimo returning from a successful fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the Eskimo exerts a force of 1.20 x102 N on the sled by pulling on the rope.
Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

15. (a) How much work does he do on the sled if the rope is horizontal to the ground ( 0° in Figure 5.6) and he pulls the sled 5.00 m? (b) How much work does he do on the sled if ° and he pulls the sled the same distance?
Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

16. Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

17. Answers:
600 J
520 J
Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

18. Work and Dissipative Forces
Work can be done by friction
The energy lost to friction by an object goes into heating both the object and its environment
Some energy may be converted into sound
For now, the phrase “Work done by friction” will denote the effect of the friction processes on mechanical energy alone

19. e.g. 5.2
Suppose that in Example 5.1 the force of friction between the loaded 50.0-kg sled and snow is 98 N (a) The Eskimo again pulls the sled 5.00 m, exerting a force of 120 N at an angle of 0°. Find the net work done on the sled. (b) Repeat the calculation if the applied force is exerted at an angle of 30.0° with the horizontal.
Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

20. e.g. 5.2
Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

21. e.g. 5.2
Answers:
110 J
90 J
Figure 5.6 (Examples 5.1 and 5.2) An Eskimo pulling a sled with a rope at an angle  to the horizontal.
Fig. 5-6, p.121

22. Kinetic Energy 5.2 Energy associated with the motion of an object
Scalar quantity with the same units as work
Work is related to kinetic energy

23. Work-Kinetic Energy Theorem
When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy
Speed will increase if work is positive
Speed will decrease if work is negative

24. Work and Kinetic Energy
An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest
The moving hammer has kinetic energy and can do work on the nail

25. Figure 5.9 (Example 5.3) A braking vehicle just prior to an accident.
Work-energy Theorem allow for collision analysis. (see e.g. 5.3 on p. 124)
Fig. 5-9, p.124

26. Types of Forces (Read on own)
There are two general kinds of forces
Conservative
Work and energy associated with the force can be recovered
Nonconservative
The forces are generally dissipative and work done against it cannot easily be recovered

27. Conservative Forces (Read on own)
A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points
The work depends only upon the initial and final positions of the object
Any conservative force can have a potential energy function associated with it

28. More About Conservative Forces (Read on own)
Examples of conservative forces include:
Gravity
Spring force
Electromagnetic forces
Potential energy is another way of looking at the work done by conservative forces

29. Because the gravity field is conservative, the diver regains as kinetic energy the work she did against gravity in climbing the ladder. Taking the frictionless slide gives the same result.
Figure 5.10 Because the gravity field is conservative, the diver regains as kinetic energy the work she did against gravity in climbing the ladder. Taking the frictionless slide gives the same result.
Fig. 5-10, p.125

30. Nonconservative Forces (Read on own)
A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points.
Examples of nonconservative forces
kinetic friction, air drag, propulsive forces

31. Friction as a Nonconservative Force (Read on own)
The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature
The objects are warmer than they were before the movement
Internal Energy is the term used for the energy associated with an object’s temperature

32. Friction Depends on the Path (Read on own)
The blue path is shorter than the red path
The work required is less on the blue path than on the red path
Friction depends on the path and so is a non-conservative force

33. Potential Energy 5.3
Potential energy is associated with the position or elasticity of the object within some system
Potential energy is a property of the system, not the object
A system is a collection of objects interacting via forces or processes that are internal to the system

34. Work and Potential Energy
For every conservative force a potential energy function can be found
Evaluating the difference of the function at any two points in an object’s path gives the negative of the work done by the force between those two points

35. Gravitational Potential Energy
Gravitational Potential Energy is the energy associated with the relative position of an object in space near the Earth’s surface
Objects interact with the earth through the gravitational force
Actually the potential energy is for the earth-object system

36. Work and Gravitational Potential Energy
PE = mgy
PE=mgh
Units of Potential Energy are the same as those of Work and Kinetic Energy (J)

37. Work-Energy Theorem, Extended
The work-energy theorem can be extended to include potential energy:
If other conservative forces are present, potential energy functions can be developed for them and their change in that potential energy added to the right side of the equation

38. Reference Levels for Gravitational Potential Energy
A location where the gravitational potential energy is zero must be chosen for each problem
The choice is arbitrary since the change in the potential energy is the important quantity
Choose a convenient location for the zero reference height
often the Earth’s surface
may be some other point suggested by the problem
Once the position is chosen, it must remain fixed for the entire problem

39. Figure 5.13 Any reference level— the desktop, the floor of the room, or the ground outside the building—can be used to represent zero gravitational potential energy in the book–Earth system.
Fig. 5-13, p.128

40. e.g. 5.4
A 60.0-kg skier is at the top of a slope, as shown in Figure At the initial point A, she is 10.0 m vertically above point B. Setting the zero level for gravitational potential energy at B, find the
gravitational potential energy of this system when the skier is at A.
Figure 5.14 (Example 5.4)
Fig. 5-14, p.128

41. Figure 5.14 (Example 5.4)
Fig. 5-14, p.128

42. Answer:
5880 J
Figure 5.14 (Example 5.4)
Fig. 5-14, p.128

43. Conservation of Mechanical Energy
Conservation in general
To say a physical quantity is conserved is to say that the numerical value of the quantity remains constant throughout any physical process
In Conservation of Energy, the total mechanical energy remains constant
In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant.

44. Conservation of Energy, cont.
Total mechanical energy is the sum of the kinetic and potential energies in the system
Other types of potential energy functions can be added to modify this equation

45. Problem Solving with Conservation of Energy
Define the system
Select the location of zero gravitational potential energy
Do not change this location while solving the problem
Identify two points the object of interest moves between
One point should be where information is given
The other point should be where you want to find out something

46. Problem Solving, cont Verify that only conservative forces are present
Apply the conservation of energy equation to the system
Immediately substitute zero values, then do the algebra before substituting the other values
Solve for the unknown(s)

47. QQ 5.2
Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal, as in Active Figure Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest. (a) 1, 2, 3 (b) 2, 1, 3 (c) 3, 1, 2 (d) all three balls strike the ground at the same speed.
FIGURE 5.15 (Quick Quiz 5.2) Three identical balls are thrown with the same initial speed from the top of a building.
Fig. 5-15, p.130

48. QQ 5.2
Three identical balls are thrown from the top of a building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal, as in Active Figure Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest. (a) 1, 2, 3 (b) 2, 1, 3 (c) 3, 1, 2 (d) all three balls strike the ground at the same speed.
FIGURE 5.15 (Quick Quiz 5.2) Three identical balls are thrown with the same initial speed from the top of a building.
Fig. 5-15, p.130

49. QQ 5.3
Bob, of mass m, drops from a tree limb at the same time that Esther, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they reach the ground?
(a) Bob’s kinetic energy is greater than Esther’s.
(b) Esther’s kinetic energy is greater than Bob’s.
(c) They have the same kinetic energy.
(d) The answer depends on the shape of the slide.

50. QQ 5.3
Bob, of mass m, drops from a tree limb at the same time that Esther, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they reach the ground?
(a) Bob’s kinetic energy is greater than Esther’s.
(b) Esther’s kinetic energy is greater than Bob’s.
(c) They have the same kinetic energy.
(d) The answer depends on the shape of the slide.

51. e.g. 5.5
A diver of mass m drops from a board 10.0 m above the water’s surface, as in Figure Neglect air resistance. (a) Use conservation of mechanical energy to find his speed 5.00 m above the water’s surface. (b) Find his speed as he hits the water.
Figure 5.16 (Example 5.5) The zero of gravitational potential energy is taken to be at the water’s surface.
Fig. 5-16, p.131

52. e.g. 5.5
Figure 5.16 (Example 5.5) The zero of gravitational potential energy is taken to be at the water’s surface.
Fig. 5-16, p.131

53. e.g. 5.5
9.90 m/s
14.0 m/s
Figure 5.16 (Example 5.5) The zero of gravitational potential energy is taken to be at the water’s surface.
Fig. 5-16, p.131

54. Work-Energy With Nonconservative Forces
If nonconservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy
Often techniques from previous chapters will need to be employed

55. e.g. 5.7
Waterslides are nearly frictionless, hence can provide bored students with high-speed thrills (Fig. 5.18). One such slide, Der Stuka, named for the terrifying German dive bombers of World War II, is 72.0 feet high (21.9 m), found at Six Flags in Dallas, Texas, and at Wet’n Wild in Orlando, Florida. (a) Determine the speed of a 60.0-kg woman at the bottom of such a slide, assuming no friction is present. (b) If the woman is clocked at 18.0 m/s at the bottom of
the slide, how much mechanical energy was lost through friction?
Figure 5.18 (Example 5.7) If the slide is frictionless, the speed of the thrill seeker at the bottom depends only on the height of the slide, not on the path it takes.
Fig. 5-18, p.132

56. e.g. 5.7
Figure 5.18 (Example 5.7) If the slide is frictionless, the speed of the thrill seeker at the bottom depends only on the height of the slide, not on the path it takes.
Fig. 5-18, p.132

57. e.g. 5.7
20.7 m/s
-3160 J
Figure 5.18 (Example 5.7) If the slide is frictionless, the speed of the thrill seeker at the bottom depends only on the height of the slide, not on the path it takes.
Fig. 5-18, p.132

58. Potential Energy Stored in a Spring 5.4
Involves the spring constant, k
Hooke’s Law gives the force
F = - k x
F is the restoring force
F is in the opposite direction of x
k depends on how the spring was formed, the material it is made from, thickness of the wire, etc.

59. Potential Energy in a Spring
Elastic Potential Energy
related to the work required to compress (or stretch) a spring from its equilibrium position to some final, arbitrary, position x

60. Work-Energy Theorem Including a Spring
Wnc = (KEf – KEi) + (PEgf – PEgi) + (PEsf – PEsi)
PEg is the gravitational potential energy
PEs is the elastic potential energy associated with a spring
PE will now be used to denote the total potential energy of the system

61. Conservation of Energy Including a Spring 5.5
The PE of the spring is added to both sides of the conservation of energy equation
The same problem-solving strategies apply

62. Nonconservative Forces with Energy Considerations
When nonconservative forces are present, the total mechanical energy of the system is not constant
The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system

63. Nonconservative Forces and Energy
In equation form:
The energy can either cross a boundary or the energy is transformed into a form of non-mechanical energy such as thermal energy

64. Transferring Energy By Work By applying a force
Produces a displacement of the system

65. Transferring Energy Heat
The process of transferring heat by collisions between molecules
For example, the spoon becomes hot because some of the KE of the molecules in the coffee is transferred to the molecules of the spoon as internal energy

66. Transferring Energy Mechanical Waves
A disturbance propagates through a medium
Examples include sound, water, seismic

67. Transferring Energy Electrical transmission
Transfer by means of electrical current
This is how energy enters any electrical device

68. Transferring Energy Electromagnetic radiation
Any form of electromagnetic waves
Light, microwaves, radio waves

69. Notes About Conservation of Energy
We can neither create nor destroy energy
Another way of saying energy is conserved
If the total energy of the system does not remain constant, the energy must have crossed the boundary by some mechanism
Applies to areas other than physics

70. Power 5.6
Often also interested in the rate at which the energy transfer takes place
Power is defined as this rate of energy transfer
SI units are Watts (W)

71. Power, cont. US Customary units are generally hp
Need a conversion factor
Can define units of work or energy in terms of units of power:
kilowatt hours (kWh) are often used in electric bills
This is a unit of energy, not power

72. Center of Mass
The point in the body at which all the mass may be considered to be concentrated
When using mechanical energy, the change in potential energy is related to the change in height of the center of mass

73. Work Done by Varying Forces 5.7 (Don’t do this section)
The work done by a variable force acting on an object that undergoes a displacement is equal to the area under the graph of F versus x

74. Spring Example
Spring is slowly stretched from 0 to xmax
W = ½kx²

75. Spring Example, cont.
The work is also equal to the area under the curve
In this case, the “curve” is a triangle
A = ½ B h gives W = ½ k x2